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Ta có :
\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right).....\left(1-\frac{1}{10^2}\right)\)
\(=\)\(\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}.....\frac{10^2-1}{10^2}\)
\(=\)\(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{9.11}{10.10}\)
\(=\)\(\frac{1.3.2.4.3.5.....9.11}{2.2.3.3.4.4.....10.10}\)
\(=\)\(\frac{\left(1.2.3.....9\right).\left(3.4.5.....11\right)}{\left(2.3.4.....10\right).\left(2.3.4.....10\right)}\)
\(=\)\(\frac{11}{2.10}\)
\(=\)\(\frac{11}{20}\)
Chúc bạn học tốt ~
(1-1/2^2)(1-1/3^2)(1-1/4^2)....(1-1/10^2)
=3/4.8/9.15/16...99/100
Từ đó tính kết quả là ok
\(A=4+\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{19}\right)\cdot\left(1-\frac{1}{20}\right)\)
\(A=4+\left(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{18}{19}\cdot\frac{19}{20}\right)\)
\(A=4+\frac{1\cdot2\cdot3\cdot...\cdot18\cdot19}{2\cdot3\cdot4\cdot...\cdot19\cdot20}\)
\(A=4+\frac{1}{20}\)
\(A=\frac{81}{20}\)
Bạn tự viết lại đề bài nha
\(\frac{1}{2}\)x\(\frac{2}{3}\)x\(\frac{3}{4}\)x\(\frac{4}{5}\)x...x\(\frac{18}{19}\)x\(\frac{19}{20}\)
=\(\frac{1x2x3x4x...x18x19}{2x3x4x5x...x19x20}\)
=\(\frac{1}{20}\)
= \(\frac{1}{2}\). \(\frac{2}{3}\).\(\frac{3}{4}\).\(\frac{4}{5}\). ... . \(\frac{18}{19}\).\(\frac{19}{20}\)
= \(\frac{1}{2}\)
tk cho mk nha, mik đg âm điểm huhu
\(8\frac{2}{7}-\left(1\frac{1}{6}+25\%\right)=\frac{58}{7}-\left(\frac{7}{6}+\frac{1}{4}\right)=\frac{58}{7}-\frac{17}{12}=\frac{577}{84}\)
\(4\frac{3}{4}+\left(-0,37\right)+\left(-1,28\right)+\left(-2,5\right)+3\frac{1}{12}\)
\(=\frac{19}{4}+\left(-\frac{83}{20}\right)+\frac{37}{12}=\frac{3}{5}+\frac{37}{12}=\frac{221}{60}\)
\(8\frac{2}{7}-\left(1\frac{1}{6}+25\%\right)=\frac{58}{7}-\left(\frac{7}{6}+\frac{1}{4}\right)=\frac{58}{7}-\frac{17}{12}=\frac{577}{84}\)
Đặt A bằng biểu thức trên
Ta có:
\(A=\left(1-\frac{4}{7}\right).\left(1-\frac{1}{8}\right).\left(1-\frac{1}{9}\right)...\left(1-\frac{1}{2011}\right)\)
\(A=\frac{3}{7}.\left(\frac{7}{8}\right).\left(\frac{8}{9}\right)...\left(\frac{2009}{2010}\right).\left(\frac{2010}{2011}\right)\)
\(A=\frac{3}{7}.\left(\frac{\left(7.8...2009.2010\right)}{\left(8.9...2010.2011\right)}\right)\)
\(A=\frac{3}{7}.\frac{7}{2011}\)\(=\frac{3}{2011}\)
Ok nhé, bài này khá dễ !
\(E=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{200}\left(1+2+....+200\right)\)
\(=1+\frac{1}{2}.\frac{2.3}{2}+\frac{1}{3}.\frac{3.4}{2}+....+\frac{1}{200}.\frac{200.201}{2}\)
\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+....+\frac{201}{2}\)
\(=\frac{2+3+4+...+201}{2}\)
\(=\frac{\frac{201.202}{2}-1}{2}=10150\)
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{50}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{49}{50}\)
\(=\frac{1}{50}\)
Chỗ nào không hiểu nhắn tin cho tớ nha!
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{50}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{49}{50}\)
\(=\frac{1}{50}\)
Cảm ơn nhiều :D